Cho biết I=1000(USD)^16 P_(T)=5(USD/dv) P_(Q)=10(USD/dv) TU=(Q-2)T a) Xác định T=?& Q=? để TU đạt tối đa. b) Xác định phương trình đường ngân sách và vẽ đồ thị? c) Tính tỷ lệ thay thế biên của . T cho O? d) Nếu giá của hàng hóa thực phẩm (T) tǎng lên gấp đôi thì đường ngân sách thay đổi như thế nào? Xác định PA TDTU mới. Tính tổng hữu dụng tôi đa? Xác định đường cầu cá nhân đối với thực phẩm

<p> <br />1. To find the values of \(T\) and \(Q\) that maximize \(TU\), we need to understand the given equations and constraints. The utility function is \(TU = (Q - 2)T\), and the budget constraint is given by \(I = P_T T + P_Q Q\), where \(I\) is the income, \(P_T\) and \(P_Q\) are the prices of goods \(T\) and \(Q\), respectively.<br /><br />2. The budget equation can be derived from the given values: \(I = 1000\) USD, \(P_T = 5\) USD/dv, and \(P_Q = 10\) USD/dv. The budget equation is \(1000 = 5T + 10Q\).<br /><br />3. To maximize \(TU\), we can use the method of Lagrange multipliers, which is a strategy for finding the local maxima and minima of a function subject to equality constraints.<br /><br />4. The marginal rate of substitution (MRS) of \(T\) for \(Q\) is the rate at which a consumer can give up some amount of \(T\) in exchange for \(Q\) while maintaining the same level of utility. It is calculated as the negative of the ratio of the marginal utilities of \(T\) and \(Q\).<br /><br />5. If the price of \(T\) doubles, the new budget constraint will be \(1000 = 10T + 10Q\). This change will affect the consumer's choice of \(T\) and \(Q\) and thus the maximum utility.<br /><br />6. To find the new maximum utility and the individual demand curve for the food item \(T\), we need to solve the utility maximization problem with the new budget constraint.<br /><br />7. The individual demand curve for a good shows the quantity of the good a consumer will buy at each price level, holding other factors constant. It can be derived from the utility maximization problem.<br /><br />To solve these parts, we will use mathematical economics techniques, particularly optimization and algebra.</p>